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From "David Hoffer" <david.hof...@issinc.com>
Subject RE: commons-math usage to calculate APR?
Date Sat, 16 Aug 2008 21:53:04 GMT
Hum, simple I'm sure but perhaps calculating APR is not quite that simple;
you have to factor in loan expenses (that's why APR is not the same as
interest rate).

I think it is something like:

P' = (P+E)I(1+i)^n/(1+i)^n

Then you solve for APR with the non-linear function which is something like:

((a(1+a)^n)-(P'/P))/((1+a)^n-1) = 0

Where a=ARR/12

Calculating P' is straightforward.  Solving for a is where I'm not clear,
plus I'm not certain of the math above. 

-Dave

-----Original Message-----
From: Bear Giles [mailto:bgiles@coyotesong.com] 
Sent: Saturday, August 16, 2008 3:40 PM
To: Commons Users List
Subject: Re: commons-math usage to calculate APR?

There are closed-form expressions for that, although I don't have them 
off the top of my head.  Something like

   m = P / (1 - i)^n

or maybe

  m = P / ((1 + i)^n - 1)

where m is monthly payment, P is principal, i is monthly interest, n is 
number of months.  It's definitely not very complex for a simple 
fixed-term, fixed-rate loan.

Bear

David Hoffer wrote:
> My usage is for USA only at this point.  
>
> I have inputs of loanAmount, monthlyInterestRate, numberMonths, loanFees;
so
> this would be for fixed monthly payments.  
>
> I understand that commons-math doesn't have specific finance methods
however
> I think the APR formula is a non-linear equation that I was hoping
> commons-math could help solve.
>
> -Dave
>
> -----Original Message-----
> From: Luc Maisonobe [mailto:Luc.Maisonobe@free.fr] 
> Sent: Saturday, August 16, 2008 2:45 PM
> To: Commons Users List
> Subject: Re: commons-math usage to calculate APR?
>
> David Hoffer a écrit :
>   
>> Can anyone point me to an example of how to use commons-math to calculate
>> APR (Annual Percentage Rate)?  
>>     
>
> There are no specific finance related algorithm in commons-math.
>
>   
>> I think this is solvable using either the NewtonSolver or BisectionSolver
>> but I am not sure how to accomplish this.  Perhaps a different way is
>> better.  
>>     
>
> I think so, but it depends on what you really need. APR computation
> seems to be slightly different depending on local regulations (for
> example USA or EU). It also depends on the assumptions you do and the
> input data. For example you can compute it one way for fixed monthly
> payments and another way for varying monthly payments.
>
>   
>> Any help would be greatly appreciated.
>>     
>
> Could you explain your needs more precisely ?
>
> Luc
>   

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